Optical spatial cloaking has captured the imagination of both the popular culture and scientific communities (see, e.g., Gbur, G. Invisibility physics: Past, present, and future. Progress in Optics 58, 65-114 (2013)). Seminal works in optical spatial cloaking includes work by Leonhardt (Leonhardt, U. Optical conformal mapping. Science 312, 1777-1780 (2006)) and Pendry, Schurig, and Smith (Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780-1782 (2006)). These seminal works provide a theoretical framework to create a curved space for light waves, by carefully constructing materials in Cartesian space. This new field of research has been called ‘transformation optics’ (McCall, M. Transformation optics and cloaking Contemporary Physics 54, 273-286 (2013)). Experimental realization of such transformational optics has been difficult, due to the previously perceived need for artificial electric and magnetic materials (called ‘metamaterials’), the narrow-band spectrum involved, infinite phase velocity (or negative index to compensate this), and anisotropy in the theory (Gbur, G. Invisibility physics: Past, present, and future. Progress in Optics 58, 65-114 (2013)). Nonetheless, inspired by transformation optics, there have been some advances in optical spatial cloaking. These advances include a two-dimensional microwave cloak (Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977-980 (2006)); a ‘carpet cloak’ that hides an object under a surface (Li, J. S. & Pendry, J. B. Hiding under the carpet: A new strategy for cloaking Physical Review Letters 101, 203901 (2008)); and even cloaking in time (Fridman, M., Farsi, A., Okawachi, Y. & Gaeta, A. L. Demonstration of temporal cloaking Nature 481, 62-65 (2012)), and (Lukens, J. M., Leaird, D. E. & Weiner, A. M. A temporal cloak at telecommunication data rate. Nature 498, 205-208 (2013)). A few groups have been able to cloak millimeter- to centimeter-sized objects as well, using birefringent materials (Zhang, B. L., Luo, Y. A., Liu, X. G. & Barbastathis, G. Macroscopic invisibility cloak for visible light. Physical Review Letters 106, 033901 (2011)), and (Chen, X. Z. et al. Macroscopic invisibility cloaking of visible light. Nature Communications 2, 176 (2011)).
To overcome the metamaterial requirements (in some implementations) and to extend cloaking to a broadband, visible regime for large objects, researchers have recently looked to ray optics for cloaking (see, e.g., Chen, H. et al. Ray-optics cloaking devices for large objects in incoherent natural light. Nature Communications 4, 2652 (2013); Zhai, T. R., Ren, X. B., Zhao, R. K., Zhou, J. & Liu, D. H. An effective broadband optical ‘cloak’ without metamaterials. Laser Physics Letters 10, 066002 (2013); and Howell, J. C., Howell, J. B. & Choi, J. S. Amplitude-only, passive, broadband, optical spatial cloaking of very large objects. Applied Optics 53, 1958-1963 (2014)). In these cloaks, the amplitude and direction of light fields are considered, as opposed to the full preservation of fields (amplitude and phase) of transformation optics. These designs have been able to cloak centimeter to meter-sized objects with commonly available optics. Yet, these schemes work only for unidirectional incident light, as they are not designed for continuous multidirectional cloaking, and can have non-unity magnifications. For off-axis, non-zero angles, the background images show distortion and positional shifts. This is particularly true if the background is far away from the cloaking device. In addition, as seen in FIG. 1 of Howell, J. C., Howell, J. B. & Choi, J. S. Amplitude-only, passive, broadband, optical spatial cloaking of very large objects. Applied Optics 53, 1958-1963 (2014), rays that propagate through the system, but go through the center at non-zero angles, can actually enter the cloaking region, effectively uncloaking the space.
Despite the advances in cloaking, a 3-D multidirectional cloak has been elusive. As shown by Wolf and Habashy (Wolf, E. & Habashy, T. Invisible bodies and uniqueness of the inverse scattering problem. Journal of Modern Optics 40, 785-792 (1993)) and Nachman (Nachman, A. I. Reconstructions from boundary measurements Annals of Mathematics 128, 531-576 (1988)), no isotropic cloaking scheme can hide an object from all viewing angles. Their work answered a question that stemmed from Devaney (Devaney, A. J. Nonuniqueness in inverse scattering problem. Journal of Mathematical Physics 19, 1526-1531 (1978)), who elegantly showed how to mathematically construct potentials that have zero scattering fields, and are hence invisible. Devaney's result, however, was for a finite number of discrete directions, and not for a continuous range of angles.